Rectified great stellated hecatonicosachoron
Rectified great stellated hecatonicosachoron  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Ragishi 
Coxeter diagram  o5/2x3o5o () 
Elements  
Cells 

Faces 

Edges  3600 
Vertices  720 
Vertex figure  Semiuniform Pentagonal prism, edge lengths 1 (base) and (√5–1)/2 (side) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angle  Gid–5/2–gid: 144° Ike–3–gid: 120° 
Central density  20 
Number of external pieces  5160 
Level of complexity  20 
Related polytopes  
Army  Rox, edge length 
Regiment  Ragishi 
Conjugate  Rectified grand hecatonicosachoron 
Convex core  Hecatonicosachoron 
Abstract & topological properties  
Flag count  43200 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  H_{4}, order 14400 
Convex  No 
Nature  Tame 
The rectified great stellated hecatonicosachoron, or ragishi, is a nonconvex uniform polychoron that consists of 120 icosahedra and 120 great icosidodecahedra. Two icosahedra and five great icosidodecahedra join at each pentagonal prismatic vertex. As the name suggests, it can be obtained by rectifying the great stellated hecatonicosachoron.
Gallery[edit  edit source]
Vertex coordinates[edit  edit source]
The vertices of a rectified great stellated hecatonicosachoron of edge length 1 are given by all permutations of:
 ,
 ,
along with even permutations of:
 ,
 ,
 ,
 .
Related polychora[edit  edit source]
The rectified great stellated hecatonicosachoron is the colonel of a regiment with 15 members. Of these, one other besides the colonel itself is Wythoffian (the rectified grand stellated hecatonicosachoron), two are hemiWythoffian (the small pentagrammal antiprismatoverted dishecatonicosachoron and pentagonal retroprismatoverted hexacosihecatonicosachoron), and one is noble (the great retropental hecatonicosachoron).
It has the same circumradius as the hexagonaldecagrammic duoprism.
Uniform polychoron compounds composed of rectified great stellated hecatonicosachora include:
 Rectified great stellated diacositetracontachoron (2)
 Rectiied great stellated chirohexacosichoron (5)
 Rectified great stellated dishexacosichoron (10)
External links[edit  edit source]
 Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#103).
 Klitzing, Richard. "ragishi".